When a conventional wire electric discharge machining apparatus machines a workpiece using a wire, a wire guide having a nozzle delivers a machining fluid to the wire. This wire electric discharge machining apparatus detects an amount of displacement of the wire caused by a pressure of the machining fluid and determines a position correction amount of the wire based on the detected displacement amount. The wire electric discharge machining apparatus then corrects a relative position between the workpiece and the wire by using the position correction amount, thereby correcting a machining contour error (see, for example, Patent Literature 1).